1. Field of the Invention
The invention to which this application relates is broadcast receiver apparatus and a method of using the same wherein high performance channel estimation is enabled while minimising complexity.
2. Prior Art
Coherent communication systems are desirable for their theoretically and practically achievable high data rate, particularly when applied in Multi Input Multi Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems in which channel estimation is a significant task to achieve high performance.
Fast fading channels are of particular interest as they represent mobile scenarios. Pilot symbol aided multiplexed (PSAM) channel estimation methods are of particular interest for fast fading channels in order to track channel variation. Many existing PSAM channel estimation methods are too computationally complex to be implemented, for example minimum mean square error (MMSE) where channel statistics and noise variance are required to be known or estimated a priori. Others, although low in complexity, often lack performance, for example least squares (LS) channel estimator
Least squares (LS) channel estimation for MIMO-OFDM, although widely applicable for its low complexity, often involves the poorly-conditioned matrix inverse problem. The inverse solution of such a poorly-conditioned matrix can significantly degrade the overall system performance as it causes large channel estimation errors which have considerable adverse influence on system performance.
The following notation is used hereinafter:                E{•} denotes the statistical expectation;        (•)T, (•)t and (•)t stand for transpose, pseudoinverse and hermitian operators respectively;        rank {•} and Tr{•} denote the rank and trace;        diag[x]stands for the diagonal matrix whose diagonal is x;        IN denotes N×N identity matrix.        
A linear statistical model consists of an observation (y) that includes a model of signal component (x) and an error or noise component (w). This leads to a typical model expression:y=x+w where x=Ph where P is the model matrix and h is the parameter vector. The above expression indicates that we are trying to estimate h from noisy observations y. Computation of least squares estimate of h will require to solve the signal inverse problem by computing the solution of a linear set of equations. The solution is then given by minimizing (y−Pĥ)T(y−Pĥ), leading to the well known analytical solution of a form ĥ=(PTP)−1PTyĥ=Pty, where Pt is the pseudo-inverse of P.
When structuring the solution of the inverse problem by SVD factorization of Pt we get:
                                                                        h                ^                            =                                                P                  †                                ⁢                y                                                                                        =                                                W                  ⁢                                                            ∑                                              -                        1                                                              ⁢                                                                                  ⁢                                                                  U                        T                                            ⁢                      y                                                                      =                                                                                        =                                                ∑                  i                                                                                        ⁢                                                                  ⁢                                                      w                    i                                    ⁢                                      1                                          s                      i                                                        ⁢                                      u                    i                    T                                    ⁢                  y                                                                                        (        a        )            where W and V are unitary matrices consisting of columns wi and vt, respectively and Σ is a matrix comprised of singular values (SV) of P on its diagonal. Here it is evident that the solution may be highly noise sensitive because of the possible small singular values si in the singular values decomposition (SVD). The small singular values imply that P is poorly-conditioned for si□1&si≠0 (when si=0, P is ill-conditioned), a common phenomenon in inverse problems. The poorly-conditioned P will introduce numerical stability problems to the model and degrades significantly the performance merit.
The process of computing the solution of the linear set of equations with poorly-conditioned set matrix is numerically highly unstable, in which case the estimate may be highly noise sensitive. Poorly-conditioned matrix inverse problems require regularization to prevent the solution estimate from being sensitive to noise in the data, otherwise the noise in the data is amplified in the solution estimate. This is the case for all inverse systems including the LS channel estimation method for MIMO-OFDM that typically involves large matrix inversion.
An aim of the present invention is to provide high performance channel estimation while minimising complexity.